9514 1404 393
Answer:
- [-4, -1)
- [-1, 1)
- [1, 5]
Step-by-step explanation:
The numbers that describe the domain of the piece are the x-value at the left end and the x-value at the right end of each piece.
Piece 1 is defined between x=-4 and x=-1, so the interval is [-4, -1).
Piece 2 is defined between x=-1 and x=1, so the interval is [-1, 1).
Piece 3 is defined between x=1 and x=5, so the interval is [1, 5].
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<em>Additional comment</em>
The rounded bracket at the right end of the domain interval means the point is not included. The square bracket means the point is included. In general, you only want each x-value to have one corresponding f(x) definition, so it is usually not appropriate to include it as part of two different pieces of the piecewise function. [-4, -1) means -4 ≤ x < -1.
Answer:
Step-by-step explanation:
p = 0.05 ( or 5%)
n = 12
Part b)
Expected value = n X p
expected value = 12 X 0.05
Expected value = 0.60
Part c)
Batch will be accepted if the number of defectives is less than 2
P(accepted) = P( x = 0) + P (x = 1)
where x = number of defectives
From binomial formula;
P(X=x) = nCx X p^x X (1-p)^(n-x)
we got n = 12, p = 0.05
P(x=0) = 12C0 X 0.05^0 X (0.95)^12
P(x=0) = 0.54036
P(x=1) = 12C1 X (0.05)61 X (0.95)^11
P(x=1) = 0.34128
P(accepted) = 0.54036 + 0.34128
P(accepted) = 0.88164
Part d)
Standard deviation = √(0.05 X 0.95/12) = 0.062915
Answer:
Step-by-step explanation:
This question has missing detail. (See attachment for the data)
Required
Determine the probability that a selected individual who has the disease test negative.
This type of probability is referred to as conditional probability.
First, we need to get the number of individuals who have the disease.
Next, we list out the number of individual who have the disease but is negative.
The probability is then calculated as:
<em>(approximated)</em>
The answer is B)
16y^2-x^2 also simplifies into
(4y+x)(4y-x)
Hey there! I'll try to provide you with my best answer.
Answer: ∠a is 20° , ∠b is 130° and ∠c is 50°
If you see more precisely then ΔABC is a complete triangle. And we know that a triangle is 180°. So in respect to ΔABC, we know ∠A and ∠C. So ∠B remains.
∠A is 60° + 30° = 90°
∠C is 70°
∠B is 90° + 70° + ∠B = 180°
∠B + 160° = 180°
∠B = 180° - 160°
∠B = 20°
Now we know that angle a (the corner angle) is 20°. Remaining is angle b and angle c. The ones we actually have to find in the question given.
In one of the small triangle which the,"b" is.
We know ∠a is 20° and the other side is 30°. So the same formula applies again.
∠a + 30° + ∠b = 180°
20° + 30° + ∠b = 180°
∠b + 50° = 180°
∠b = 180° - 50°
∠b = 130°
Now ∠c is remaining. Well all the angles are given again so.. same!
∠c + 60° + 70° = 180°
∠c + 130° = 180°
∠c = 180° - 130°
∠c = 50°
There is another easier way to find ∠c. Line B and C is a straight line so a straight line is also 180°. We know ∠b is 130° so instead of subtracting and switching so much, we can directly subtract it from 180 because they are on a straight line.
∠b + ∠c = 180°
130° + ∠c = 180°
∠c = 180° - 130°
∠c = 50°
The answer is same at the end. Even though this is easier cause we can mentally subtract it instead of going to the triangle formula.
Note: When i show angles with capital letters and small letters, there is a difference. ∠B and ∠b is not the same thing when I wrote it. So please do not misunderstand it. The capital and small letters are clearly shown in the image you have shown.
And sorry for making it so long. I just hope you understood it clearly!! ^^